Associate Professor of MIE @Northeastern. Interested in control theory, optimization, math, and puzzles. The glass is twice as large as it needs to be.
My contribution to the #Wordle discourse, with help from @VincentTjeng and @evanrsparks.
A definitive look at the game: insights, heuristics, optimal strategies, and the limits of what is possible.
https://t.co/jSRXV1BYr5
Can your AI keep up with dynamic attackers? In a paper to appear at #AISTATS2025 with @avibose22@LaurentLessard and Maryam Fazel, we study robustness to learning algorithms to dynamic data poisoning attacks that can adapt attacks while observing the progress of learning
@gravity_levity It doesn't decay quite that quickly, but it's still fast:
P(1) ~ 1/k!
So basically: -log(P(1)) = O(k*log(k))
rather than: -log(P(1)) = O(k^2),
which is what you had conjectured.
This week's #Fiddler puzzle is a random walk: From (k), you hop to (k-1) with probability 1/k and hop to (k+1) otherwise. If you start at (2), what is the probability you eventually hop to (1)?
I wrote a short tutorial here:
https://t.co/V0QhIIEiLw
This week's #fiddler: Assign distinct prime numbers to the vertices of a dodecahedron so the sum of the vertices of each face sum to 2025. I modeled this as an integer linear program. Here is one possible solution. @xaqwg
My write-up: https://t.co/vFbpDurcNP
Hey @AerLingus I'm on a flight from Dublin to Boston and we've been stuck on the tarmac at @loganairports after landing for TWO HOURS (and counting). Apparently other planes are being de-iced which is preventing us from deplaning...
The pilot keeps saying there is "nothing he can do". You mean to tell me there are no other gates available at the airport? We can't deplane on the tarmac? This is a full flight with 8 seats across and we've been on this plane for almost 10 hours now.
This week's #Fiddler: what is the minimum-energy way to pack 9 particles in a square box, where energy is measured as the sum of 1/dist over all pairs of particles?
Turns out it's NOT a regular 3x3 lattice! @xaqwg
write-up:
https://t.co/tBfK0Jy2yq
Halloween #fiddler puzzle: A bag contains N Reese's cups and an unknown number of candy corn pieces. You reach into the bag k ≤ n times at random and pull out a Reese's each time! How many candy corn do you expect to be in the bag? @xaqwg
My write-up:
https://t.co/z2DxoGC9xr
This week's #Fiddler by @xaqwg: if x1,...,xn are uniform on [0,1], find the probability that
round(x1)+...+round(xn) = round(x1+...+xn)
It's not so simple! Here's a visualization of n=4, (hypercube slices), for which the answer is 115/192
My write-up:
https://t.co/BPiDlhtvY0
New preprint with Joao Cavalcanti and @Ashia__Wilson!
https://t.co/gkaAWYvoBd
tl;dr: If you make your backtracking line search routine ADAPTIVE, you get faster continuous optimization algorithms with no additional computational burden!
Longer summary below!🧵
One such example (we discuss others in the paper) is quasi-Newton methods. For these methods, line search serves the purpose of guaranteeing global convergence rather than finding a "best" step size. Once we enter a local convergence regime, adjustments are no longer beneficial.